Radiochemistry and Nuclear Methods of Analysis

WILLIAM D. EHMANN

Professor, Department of Chemistry University of Kentucky Lexington, Kentucky

DIANE E. VANCE

Staff Development Scientist Analytical Services Organization

Oak Ridge Y-12 Plant Oak Ridge, Tennessee

A WILEY-INTERSCIENCE PUBLICATION

JOHN WILEY & SONS, INC.

New York / Chichester / Brisbane / Toronto / Singapore

*.

CONTENTS

CHAPTER 1 INTRODUCTION TO RADIOCHEMISTRY 1

1.1. The Discovery of Radioactivity and Evolution of Nuclear Theory 1

1.2. Forces in Matter and the Subatomic Particles 20 1.2.1. Forces in Nature 20 1.2.2. The Subatomic Particles 21

1.3. Nuclides and Natural Decay Chains 22 1.3.1. Nuclides and Symbols 23 1.3.2. Classification of Nuclides 23 1.3.3. Chart of the Nuclides 25 1.3.4. Natural Decay Chains 28 1.3.5. An Extinct Natural Decay Chain 31

CHAPTER 2 TYPES OF RADIOACTIVE DECAY 35

2.1. Alpha-Particle Decay 36 2.2. Beta Decay 41

2.2.1. Negatron Decay 41 2.2.2. Positron Decay 43 2.2.3. Electron Capture (EC or e) 45

2.3. Gamma Decay 46 2.3.1. Pure Gamma-Ray Emission 48 2.3.2. Internal Conversion (IC) 48 2.3.3. Pair Production (PP) 49

2.4. Branching Decays and Decay Schemes 50 2.5. Less Common Decay Modes 50

2.5.1. Spontaneous Fission Decay 50 2.5.2. Delayed-Neutron Emission 52 2.5.3. Delayed-Proton Emission 53 2.5.4. Double-Beta Decay <- 53 2.5.5. Two-Proton Decay 54 2.5.6. 14C and Other Cluster Emission Decay 54

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Xll CONTENTS

CHAPTER 3 NUCLEAR CHEMISTRY AND MASS-ENERGY RELATIONSHIPS 57

3.1. Description of the Nucleus 57 3.2. Nuclear Properties 61

3.2.1. Angular Momentum and Nuclear Spin 61 3.2.2. Magnetic Moment (/A) 61 3.2.3. Parity and Symmetry 62

3.3. Models of Nuclear Structure 62 3.3.1. Shell Model (Single Particle Model) 63 3.3.2. Fermi Gas Model 65 3.3.3. Liquid Drop Model 66 3.3.4. Optical Model (Cloudy Crystal Ball Model) 67 3.3.5. Collective Model 67

3.4. Mass-Energy Relationships 67 3.4.1. Mass-Energy Equivalence 68 3.4.2. Energy Changes in Nuclear Reactions 69 3.4.3. Energy Changes in Radioactive Decay 74 3.4.4. Closed-Cycle Decay for Mass-Energy Calculations 75 3.4.5. Semiempirical Binding Energy Equation 76 3.4.6. Nuclear Energy Surface Diagrams 78

CHAPTER 4 NUCLEAR REACTIONS 85

4.1. Types of Nuclear Reactions 85 4.1.1. Scattering Reactions 85 4.1.2. Other Reactions 86

4.2. Energetics of Nuclear Reactions 87 4.2.1. Momentum Correction 88 4.2.2. Coulomb Barrier Correction 89

4.3. Cross Sections for Nuclear Reactions 90 4.3.1. Measurement of Cross Section 92 4.3.2. Excitation Functions 96

4.4. Reaction Mechanisms 100 4.4.1. Compound-Nucleus Formation 100 4.4.2. Direct Interactions 102

4.5. Special Nuclear Reactions 103 4.5.1. Neutron-Induced Fission 103 4.5.2. Fusion 106

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4.5.3. Heavy-Ion Reactions 107 4.5.4. Photonuclear Reactions 107

CHAPTER 5 RATES OF NUCLEAR DECAY 113

5.1. Rates of Radioactive Decay 113 5.1.1. Half-life and Average Life 114

5.2. Units of Radioactive Decay 116 5.3. Branching Decay 118 5.4. Experimental Methods for Determination of Half-life 119

5.4.1. Long Half-lives 119 5.4.2. Medium Half-lives 124 5.4.3. Short Half-lives 127 5.4.4. Very Short Half-lives 129

5.5. Estimation of Half-life from Theory and Systematics 131 5.6. Growth of Radioactive Products in a Decay Chain 133

5.6.1. Parent with a Single Radioactive Daughter 134 5.6.2. Parent with Multiple Radioactive Daughters 138

5.7. Growth of Products in a Neutron Flux 140

CHAPTER 6 INTERACTIONS OF RADIATION WITH MATTER 147

6.1. Modes of Interaction 147 6.2. Heavy Charged-Particle Interactions 149

6.2.1. Range Relationships for Heavy Charged Particles 149 6.2.2. Stopping Power 154

6.3. Beta-Particle Interactions 154 6.3.1. Range Relationships for Beta Particles 156 6.3.2. The Feather Method 158 6.3.3. Bremsstrahlung Radiation 160 6.3.4. Cerenkov Radiation 161 6.3.5. Beta Backscatter 161 6.3.6. Positron Interactions 161

6.4. Gamma-Ray Interactions 162 6.4.1. Photoelectric Effect 162 6.4.2. Compton Scattering 164 6.4.3. Pair Production 167 6.4.4. Mathematics of Gamma-Ray Absorption 170

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CHAPTER 10 RADIOTRACER METHODS 313

10.1. General Aspects of Radiotracer Use 313 10.1.1. Assumptions Made in Tracer Studies 313 10.1.2. Factors in the Choice of a Radiotracer 314 10.1.3. Production of Radiotracers 315 10.1.4. Advantages and Disadvantages of Radiotracer Use 316

10.2. Isotope Dilution Analysis 318 10.2.1. Theory and Calculations for DIDA 318 10.2.2. Applications of IDA 319 10.2.3. Variations of IDA 321

10.3. Tracers in the Study of Chemical Processes 323 10.3.1. Equilibrium Processes 323 10.3.2. Analytical Applications 325 10.3.3. Studies of Reaction Mechanisms 327

10.4. Other Applications of Radiotracers and Radionuclides 327 10.5. Nuclear Medicine and Pharmacy 331

10.5.1. General Aspects of Radiopharmaceutical Use 331 10.5.2. Nuclear Properties of Indicator Nuclides 332 10.5.3. In Vivo Diagnostic Procedures 338 10.5.4. In Vitro Diagnostic Testing: Radioimmunoassay 340 10.5.5. Therapeutic Uses of Radiation 342

CHAPTER 11 ION BEAM ANALYSIS AND CHEMICAL APPLICATIONS OF RADIOACTIVITY 347

11.1 Particle-Induced X-Ray Emission 347 11.1.1. Overview of the PIXE Process 348 11.1.2. Projectile Acceleration and Target Preparation 348 11.1.3. Ionization and X-Ray Emission 351 11.1.4. Detection and Analysis of X Rays 351 11.1.5. Applications of PIXE 353 11.1.6. PIXE Variations 354

11.2. Rutherford Backscattering Spectrometry 355 11.2.1. The Scattering Reaction 356 11.2.2. Surface Analysis Using RBS 357 11.2.3. Depth Profiling Using RBS 359 11.2.4. Channeling Effects 362 11.2.5. Applications of RBS 363

CONTENTS xvu

11.3. Mössbauer Spectroscopy 364 11.4. Hot-Atom Chemistry 367

11.4.1. Production of Hot Atoms 369 11.4.2. Energy Calculations 369 11.4.3. Applications of Hot-Atom Reactions 371

11.5. Radiation Chemistry 373

CHAPTER 12 NUCLEAR DATING METHODS 379

12.1. General Principles of Nuclear Dating Methods 379 12.2. Radiocarbon Dating 382 12.3. Tritium Dating 386 12.4. U-Pb and Th-Pb Methods 387

12.4.1 Simple He Accumulation Method 387 12.4.2. Single-Decay-Chain Methods 387 12.4.3.. Pb-Pb Method 389

12.5. Rb-Sr Method 391 12.6. K-Ar Method 395

12.6.1. Standard Method 395 12.6.2. Incremental Heating Method 395

12.7. Pleochroic Halos 397 12.8. Fission Tracks 397 12.9. Special Methods 399

12.9.1. Cosmic-Ray Exposure Ages of Meteorites 399 12.9.2. Terrestrial Ages of Meteorites 400 12.9.3. Extinct Natural Radionuclides 401 12.9.4. Re-Os Method 403 12.9.5. Lu-Hf Method 403 12.9.6. K-Ca Method 403

CHAPTER 13 THE ORIGIN OF THE CHEMICAL ELEMENTS 407

13.1. Cosmology 407 13.1.1. Elemental Abundances 408 13.1.2. Cosmic Abundance Curves 413

13.2. Primordial Nucleosynthesis 414 13.3. Stellar Evolution 417

13.3.1. Star Populations 417 13.3.2. Evolution of a Star 418

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13.4. Stellar Nucleosynthesis 420 13.4.1. Hydrogen Fusion 420 13.4.2. The CNO Bi-cycle 421 13.4.3. Helium Burning 423 13.4.4. Heavier Element Burning 424 13.4.5. The s-Process 426 13.4.6. The r- and p-Processes 428 13.4.7. Supernovae 430

13.5. The Solar Neutrino Problem 431 13.6. Synthesis of Be, B, and Li 433

CHAPTER14 PARTICLE GENERATORS 437

14.1. Natural Particle Sources 437 14.2. Nuclear Reactors 438

14.2.1. The Fission Process 438 14.2.2. Major Components of Reactors 444 14.2.3. Types of Reactors 450 14.2.4. Applications of Reactors 452

14.3. Accelerators: Basic Components 458 14.4. Cockroft-Walton Accelerators 461 14.5. Van de Graaff Accelerators 462 14.6. Linear Accelerators 465 14.7. Cyclotrons 466 14.8. Synchrotrons 470 14.9. Large Accelerators for Nuclear Physics Research 472

APPENDIX A STATISTICS FOR RADIOCHEMISTRY 475

APPENDIX B GENERAL REFERENCES AND

DATA SOURCES 483

APPENDIX C NUCLIDIC PROPERTIES 485

APPENDIX D USEFUL CONSTANTS AND CONVERSIONS 517

INDEX 519